Robust Watermarking Method for Colour Still Image Databases Mihai P. Mitrea1,2, Françoise J. Prêteux2, and Adriana Vlad1 1
Faculty of Electronics and Telecommunications, POLITEHNICA University, Bucharest–Romania 2 ARTEMIS Project Unit, Institut National des Télécommunications, Evry–France e-mail addresses:
[email protected],
[email protected]
ABSTRACT
This paper addresses the issues of oblivious, transparent and Stirmark robust watermarking of colour still image databases. Note that the well-known Cox and Ó Ruanaidh non-oblivious methods are devoted only to grey levels individual still images and, unfortunately, they do not survive the Stirmark attack. Besides, the Cox method allows only a single bit to be recovered at the detection side (a marked/unmarked answer is obtained). By extending and generalising the principles of the Cox and Ó Ruanaidh approaches, and by overcoming their limitations, the new oblivious method proposed in this paper allows a 64 bit message to be checked out at the detector. The message is coded according to the Spread Spectrum – Code Division Multiple Access (SS–CDMA) technique, and embedded into the most significant DCT (Discrete Cosine Transform) coefficients (except for the DC – the direct component). Applied to 1000 sequences of 32 still images, the method exhibits an excellent behaviour in terms of transparency (both fidelity and quality), robustness (JPEG compression, the change of format, scaling, print&scan, Stirmark attack) and probability of false alarm (lower than 2 × 10 −10 ). Finally, the extension towards colour video watermarking is taken into consideration; some solutions are proposed and experimental results are presented. 1. INTRODUCTION The greater the demand of image distribution across Internet, the greater the scepticism in this respect: an unlimited number of unauthorised copies may be easily done. The same problem arises when granting the access to colour image databases. Hence, to afford ownership and to track down copy-maker are major desiderata. In the last years, watermarking imposed itself as a good solution to such problems. Several publications (books [1], surveys, [2]–[7], as well as truly theoretical papers, [8]–[11]) supported watermarking as a science per–se. At a glance, to watermark means to embed some extra information into host data. This information is to be later used for several purposes such as: ownership proving, image/video indexing and retrieval, broadcast monitoring, etc. The embedded extra information is
called watermark or mark. The host data is a natural signal, such as text, audio, image or video. Watermarked data stand for (host) data which have a mark embedded. The first requirement for a common watermarking technique is to be transparent; in this respect, fidelity and quality are defined in [1]. A watermarking method features fidelity when the human observer cannot make any distinction between the marked and unmarked images. A watermarking method features quality when the marked data has no unpleasant artefacts (thought they may be noticeable). The second watermarking requirement is related to robustness; i.e., the mark should be detectable after any processing of watermarked data which does not change their meaning (e.g. after JPEG compression, resampling, rescaling, rotations). Depending on the targeted application, there is always a trade–off to be reached between transparency and robustness (generally, the greater the robustness, the worst the transparency). A watermarking method is referred to as non-oblivious when it requires the original (unmarked) data to be present at the detector and as oblivious when the original data may not be present. The present paper proposes an oblivious method to robust watermarking of colour still image databases. It relies both on Cox [12] and Ó Ruanaidh [13] non–oblivious methods. Note that these two methods are devoted to grey levels individual still images and do not survive the Stirmark [14] attack. Besides, the Cox method allows only a single bit to be recovered at the detection side (a marked/unmarked answer is obtained). Our method allows a 64 bit message to be checked out at the detector. The message is coded according to the Spread Spectrum – Code Division Multiple Access (SS–CDMA) technique [15],[16],13], and embedded into the most significant DCT coefficients (except for the DC). The method was applied to 1000 sequences of 32 colour still images and pointed to firm results, concerning transparency (fidelity as well as quality), robustness (with respect to practical all challenges in the watermarking applications, [3]), and probability of false alarm. We dealt with various kind of images: with large background area and/or a lot of details, several aspect ratios and sizes, different lightning conditions, etc.
The present paper has the following structure. Section 2 presents the nowadays frameworks and challenges in watermarking. Section 3 focuses on the novel method we propose. Section 4 is devoted to the experimental results obtained when watermarking colour still images databases as well as to the extension of the method towards colour video. Finally, Section 5 stands for the concluding remarks. 2. WATERMARKING AT A GLANCE At a glance, to watermark means to embed some extra information into a host data. The robust watermarking methods may be classified into three generations [11], according to the place where the mark is to be embedded, and to the information conveyed by the mark. These three generations may be represented as in Figs. 1.a–c. Key
W atermark
Noise Attack
+
Channel
Image
are referred to as attack. The detection requires the key and the original (unmarked) image and provides a marked/unmarked (yes/no) answer. Such a method is described in [17]. It must be mentioned that the transparency is afforded by the redundancy in the original image: the lower bit plans in the image may be changed without losing the quality. On the other hand, this redundancy also allows a successful attack: when randomly changing the lower bit planes, the mark just vanishes, see Fig. 2. The original image in Fig. 2.a is a 512× 512 pixels, 256 grey levels image. Fig. 2.b corresponds to a marked image (a 0 mean, 1 variance Gaussian sequence was added to image). Fig. 2.c stands for the image obtained out of randomly changing the 3 lowest bit planes in the marked image.
Key
Image
W atermark Detector
Yes/No
(a) Ke y
W ate rmark
N oise Attack
+
C ha nn el
T
Im age
Im age
K ey
(a)
(b)
W ate rmark Yes/N o De tector
(b) Noise Attack K ey
Ke y Chann el w ith side information (Im age)
W atermark
W atermark Detector
Rec overed L ogo
oblivious watermark
Logo
(c) Key
Logo
W atermark Im age
Noise Attack
Key
Channel
W atermark Detector
T
Recovered Logo
oblivious watermark
(d) Fig. 1: Synopsis of the three successive schemes proposed for watermarking: the first, second and third generation in Figs. 1.a, 1.b and 1.c, respectively. Fig. 1.d corresponds to the watermarking scheme advanced in the present paper. In the first generation watermarking methods, the mark consists of a (pseudo–random) 0 mean Gaussian sequence, generated according to a secret information (referred to as key). This mark is simply added to the image. The marked image is subject to two types of alterations. First, there are the perturbations which come across with any processing of the image; these perturbations are referred to as noise. Second, an unauthorised user might try to make the mark undetectable at the detection side; these perturbations
(c) Fig. 2: First generation watermarking. Fig. 2.a stands for to the original (unmarked) image, Fig. 2.b corresponds to the marked image while Fig. 2.c represents a successfully attacked image. The second generation watermarking methods do not embed the mark directly into image but into a T transform of the image (Fig. 1.b). Results concerning several transforms have already been reported in the literature: DCT, Hadamard transform, Fourier transform, Mellin–Fourier transform, wavelet, etc. Each of these transforms provides a different advantage. For instance, the methods which use the DCT transform [12] feature a very good robustness concerning the JPEG compression while methods which are based on the Mellin–Fourier [13] transform feature good invariance against rotation. To exemplify the second generation watermarking paradigm, be there the method in [12]. The mark consists of a 0 mean Gaussian sequence and is to be added into the largest DCT coefficients (except for the DC). As the largest DCT coefficients stand for the salient characteristics of the image, in order to meet the transparency requirement, the power of the mark should be quite low. For instance, such a procedure may be applied to the original in Fig. 2.a. The mark has a power σ 2 = 1 and is added into the 1024 largest
DCT coefficients (except for the DC). The corresponding marked image is depicted in Fig. 3.a. In order to illustrate the robustness, this marked image was first corrupted by an additive Gaussian noise with
µ = 30 and σ 2 = 64 , then, a JPEG compression at a Q = 60 quality factor was applied. Finally, the image was cropped, see Fig. 3.b. Note that the mark is detected out of processing Fig. 3.b together with the original image in Fig. 2.a. However, such a method is very poor from the rotation point of view: even the smallest rotation may conceal the mark. Moreover, for
the image containing large background area, a σ 2 = 1 power leads to artefacts which may be disturbing, see Figs. 3.c and 3.d: some artificial shadows may be noticed in the sky area in Fig. 3.d. When decreasing the mark power, such artefacts become less disturbing but the method loses much of its robustness. As an additional remark, note that the weak point shared by all the second generation methods is their non-obliviousness.
(a)
detection. That is, the third generation techniques deal only with oblivious watermarking. In order to benchmark the watermarking methods, Peticolas has developed [14] a procedure called Stirmark. This procedure brings into evidence some transformations which try to make it impossible for the detector to find out the mark while preserving the watermarked image unaltered from the human visual system point of view. It consists of several small transformations, successively applied: resampling, geometric (stretching, shearing, shifting, rotating) and a global bending on the image (a slight deviation of each pixel, depending on the position in image). It was found out that very few methods reported in the literature may survive a Stirmark attack. The classification into the above three generations is useful for the clarity sake. However, the methods reported in the literature may be hybrid. For instance, Ó Ruanaidh proposed [13] a non–oblivious method for individual grey level images, which affords several bits to be transmitted (a logo may be recovered). The method proposed in the present paper is also hybrid, see Fig. 1.d. It is an oblivious method which affords a message of 64 bits to be recovered at the detection without taking any advantage on the fact that the original image is known during the embedding procedure. We shall show in the next section that our method affords all the third generation requirements and the Stirmark robustness while ignoring the side information.
(b)
(c) (d) Fig. 3: Second generation watermarking: performance discussion. The original image is shown in Fig. 2.a. Fig. 3.a stands for the marked image, Fig. 3.b represents a combination of attacks: Gaussian noise addition, JPEG compression, and cropping. Fig. 3.c and Fig. 3.d present the mark power constraints: when marking the original image in Fig. 3.c, a value σ = 1 leads to visible artefacts in Fig. 3.d. The third generation watermarking techniques try to take advantage on the fact that the original image is known when embedding the mark; that is, the channel in Fig. 1.c is to be a channel with side information [18], [11]. Moreover, the channel capacity should be increased: the problem is no longer to transmit a single bit of information (as in the yes/no answer case) but to recover a logo, a name, etc, represented on several bits, e.g. [3] about 60 to 70 bits. Finally, another requirement is stated: the original (unmarked) data should not be presented at the
3. THE PROPOSED METHOD The watermarking method we propose is devoted to colour still image sequences. It will be further presented, considering a sequence of 32 individual still images. Note that all the numerical values presented below were those involved in our experiments. Depending on the targeted application, they may be adapted, without altering the method quality. The principle of our method is the following: it is known from the communication theory [15],[16],[12] that the best way in which information may be transmitted is Spread Spectrum (SS). However, when trying to use such a powerful technique in watermarking, a limitation arises: generally, we do not have at our disposal a large spectrum where the mark may be embedded. To overcome this difficulty, our method build–up a spectrum, by considering the largest 2D–DCT coefficients (except for the DCs) of each and every image in the sequence. Note that as these coefficients stand for salient characteristics of the image, they are likely to be preserved by all the transformation which keep the same quality of the images (here including the attacks). On the other hand, as the SS techniques allow a very low power signal to be detect (that is, a very low power mark to be recovered), the mark may be embedded into the largest DCT coefficients, without altering the quality of the image. Further, we shall present some details concerning the watermarking scheme we propose.
3.1. Embedding the Mark The colour images are represented in the HSV system, each component belonging to the [ 0 ,1 ] interval. The embedding procedure starts by computing the DCT for each and every V component corresponding to the images in the sequence. The coefficients are sorted in a decreasing order and the largest 1024 (except for the DC) are recorded alongside with their locations. Consequently, two vectors of N = 1024 × 32 elements are obtained; be they denoted by v (the vector corresponding to the coefficients) and by l (the vector corresponding to the locations). The mark is generated by a SS–CDMA technique, starting from the Ó Ruanaidh suggestions, [13]. Be there s1 , s 2 , ..., s16 the logo, represented as 16 digits in hexadecimal (that is, 64 bits). It is known from literature [15], [16], [13] that the performances of any CDMA system are limited by the quality of the pseudo–random generator it involves in. That is, the pseudo–random generator should provide sequences with delta–like correlation functions. There are several ways in which such generators may be implemented, [15], [16], [19]. In our experiments, we used a LFSR – Linear Feedback Shift Register, [19], [20], characterised by an m degree g ( x) polynomial which is primitive over the R T
The n sequence is further divided into 16 ni
sub–sequences, each of them having an N + 15 length: ni = [ ni,0 , ni,1 , ..., ni, N +14 ] , i = {1, 2 ... , 16 } .
Note that as the N value we involved in our experiments is large enough, the auto–correlation function corresponding to each ni sub–sequence will approximate a delta function while the cross– correlation functions between any ni and any n j , i ≠ j will be practically zero, [19], [20].
Each s i symbol in the logo is modulated by means of an N length ri sequence, cut out from the ni sequence, cf. (4) and Fig. 5: si ↔ ri = [ ni, s , ni, s +1 , ..., ni, s + N −1 ] (4) i i i
1+ x
residual algebra, T = 2 m − 1 , see Fig. 4. SET
D1 Q1
D2 Q2
+
g1
+
+ g2
Output Dm Qm
Fig. 5: Principle illustrating how to obtain the ri sequences.
g m −1
Fig. 4: A pseudo–random number generator by means of an LFSR. In Fig. 4, the feedback is closed for those polynomial coefficients which are 1 and is opened for those which are 0. The D cells are set to 1 and then the LFSR output is recorded. The output of the LFSR has a T length period iff g ( x) is primitive, [19], [20]. The 0/1 binary output of the LFSR is mapped into a bipolar (-1/+1) n sequence, (1): n = 2 × Output − 1 . (1) Be Rnn (t ) the (cyclic) auto–correlation function defined in (2): Rnn (t ) =
1 T
T −1
∑
n(τ ) ⋅ n((t + τ ) mod T ) ,
Fig. 5 exemplifies how the ri sequences are obtained; be there s1 = 2, s 2 = 4, ... , s16 = 0 . Eq. (4) means that the r1 sequence is build up from the symbols which have the ranks 2, 3, ... , N + 1 in the n1 sequence. Following the same equation, the r2 sequence is build up from the symbols which have the ranks 4, 5, ... , N + 3 in the n2 , and so on. In order to obtain the x mark, the ri sequences are summed–up, (5): 16
x=
(2)
τ =0
t = 0,1, ... , T − 1 . The n sequence has a delta–like auto–correlation function, [19], [20]: when t = 0 1 . (3) Rnn (t ) = 1 when t = 1,2,...T − 1 − T
∑ ri .
(5)
i =1
In Eq. (5), x stands for an N = 1024 × 32 length vector. Consequently, the T length of the n sequence we used must fulfil the inequality: T ≥ 16 × N = 219 , and the corresponding LFSR must be characterised by a primitive polynomial with an m degree larger than 19; in our experiments, we used m = 20 degree primitive polynomials. A larger m value would
increase the complexity but could slightly improve the method performances. Further, the power of the x mark was decreased, in order to met the transparency requirements. In our illustrations, we considered three values, namely 1 6 , 1 10 , and 1 16 (the experiments guided us to these numerical values which afford both robustness and transparency). As embedding procedure, we use the suggestions Cox made for individual grey level images, [12]: the watermarked coefficients are obtained by means of a weighted addition between the v unmarked coefficients and the x mark, (6): v' = v ⋅ ( 1 + α x ) (6) v ' represents the vector of the In Eq. (6), watermarked coefficients while α is a constant value, [12]. In our experiments, we considered α = 0.4 , [12]. This α value simply modifies the power of the x mark, with a fix amount, namely α 2 . In order to obtain the watermarked sequence, the v coefficients are replaced by the v' and 32 inverse DCTs are computed. Finally, a linear mapping was applied to the marked V components, as to ensure that they would not take values outside the [ 0 ,1 ] interval. 3.2 Detecting the Mark At the detector side, the DCTs are computed on the (possible) corrupted sequence, and the coefficients which correspond to the l recorded locations (see § 3.1) are taken into consideration; the vector obtained by concatenating these coefficients is denoted by v' ' . The detection follows the CDMA [13] procedure. The logo is recovered by means of cross–correlation functions, computed between v' ' and each ni , i = {1, 2 , ... ,16 } sub–sequence. The peak position in these cross–correlation functions represents the sˆi recovered symbol. That is, the sˆi recovered symbol is implicitly involved in (7), see also Fig. 6: Rν ' ' n ( sˆi ) = max Rν '' n (t ) , t = { 0,1, ... ,15 } . (7) i
t
i
Here, the cross–correlation functions are not delta–like, because of noise and of attacks. However, for the practical applications, the peak position is likely to keep its original position, as far as the ni sub–sequences auto–correlation functions approximate the delta function and the cross–correlation functions between ni and n j approximate zero, ∀ i ≠ j .
As a final remark, note that during the marking and the detection procedure, we dealt only with the V component (the H and S were unchanged). 4. EXPERIMENTAL RESULTS We started our experimental work by marking sequences of 32 still images. After proving the method quality, we shall extend it towards colour video. Note that this extension requires the change of the parameters. Concerning the illustrations, they are printed as grey level images; however, the reader may obtain a colour version of the images by contacting the authors. 4.1 Experimental Results on Colour Still Images In order to illustrate our method performances, we choose the original images in Fig. 7. Note that the images in Fig. 7 provide information about the way in which our method works in most difficult situations: large background areas, a lot of details, a lot of colours, etc. In order to point to the transparency, Figs. 8, 9, and 10 display the marked images, obtained when the mark power was set to 1 / 6 , 1 / 10 and 1 / 16 , respectively. It can be noticed a very good quality of the watermarking procedure we advance. However, a very good fidelity is obtained only for a mark power of 1 / 16 : some artificial shadows may be observed in the background areas in Fig. 8 and even 9 but they are no longer present in Fig. 10. Concerning robustness, a first experiment we carried out was devoted to the resistance against changing the format of the images: we found out that our method survives to practically all the formats (jpg, bmp, tiff, gif, etc). As during the embedding and detection procedures we do not take into account but the V component, our method is robust to any alteration of the hue and of the saturation in the image. To prove that, we randomly changed the H and the S components for each and every image in the sequence and we could still detect the mark. Fig. 11 illustrates such an attack on two images: one with a large background area and another one with a lot of details. To conclude with, the colour reduction robustness requirement is met by our method. Fig. 12 shows images attacked by various means: the marked image was printed (300 dpi resolution, on an usual 80g/m2 paper), scanned (at a 100 dpi resolution), cutting–down filtered (with a f 0 = 10 cut– off frequency) and then JPEG compressed at a low quality factor, namely Q = 10 . The mark survives such combination of attacks. The method also proved robustness against additive and multiplicative noise. We considered white and correlated noises, [21], with several parameters, obeying the following probability laws: Gaussian, uniform, exponential, and gamma.
Fig. 6: Principles explaining how to recover the logo.
Fig.
Fig. 7: Original (unmarked) images.
9:
Watermarked
images,
with
a
σ 2 =1 / 10 mark power.
Fig.
8:
Watermarked
σ 2 =1 / 6 mark power.
images,
with
a
Fig. 10: Watermarked images, with a
σ 2 =1 / 16 mark power.
We experimentally evaluated the P f probability of false alarm. Its upper bound depends on the σ 2 mark power, namely: Pf ≤ 3 × 10 −16 when σ 2 =1 / 6 , Pf ≤10 −11 when σ 2 =1 / 10 , and Pf ≤ 2 × 10 −10 when
Fig. 11: The effect of randomly changing the H and S components.
Fig. 12: Images attacked by print&scan, low–pass filtering, and JPEG compression. As the method we propose is based on the DCT, it is susceptible to be vulnerable to rotations. However, we found out experimentally that the mark may survives when randomly rotating each and every image in the sequence with a θ angle in the interval
θ ∈ ( − 2.5° , 2.5° ) . For larger rotations, a registration procedure should precede the detection. We also checked–up whether our method survives a Stirmark [14] attack or not, Fig. 13. Our experiment pointed out to robustness in this respect. We applied the Stirmark 3.1 attack, at its standard parameters, independently on each image in the sequence.
σ 2 =1 / 16 . As a final remark concerning the robustness, note that there is no need for all the marked images to be presented at the detection; the above–reported results are unchanged when detecting the mark out of only 24 images. Concerning an inversion attack [22], the general solutions in [22] may be used. In this context, a cryptographic mixing transformation, [23], [24] may also be considered. 4.1 Extension towards Colour Video We tried to enlarge the application field of our method from colour still image databases towards colour video. First, we replaced the still images in the sequence by successive frames in the video. All the robustness performances were preserved, but the transparency had decreased. That is, some visible artefacts had been noticed. Although these are not disturbing for several kind of video (scientific products, video surveying, etc), they may be considered unacceptable for art video. In order to obtain a good method for art video watermarking, we changed the numerical figures involved in our method. That is: • we considered sequences of 1024 successive frames; • we no longer recorded the largest 1024 DCT coefficients; instead, we skipped over the largest 128 and we recorded only the following 64; • the mark power was even smaller, namely
σ 2 = 1 / 512 ; •
after the inverse DCTs computations, we no longer used a linear mapping into [ 0 ,1 ] , because it would determine unpleasant artefacts; we considered instead a non-linear mapping we designed to preserve the same DC value for V component; that is, the V component of the marked image has the same mean value before and after mapping. The schema thus obtained has been applied on 20 video sequences and pointed to a good transparency (the artefacts are practically un-perceptible) while preserving the same robustness. However, the probability of false alarm increased; we evaluated its upper bound: P f ≤ 4 × 10 −9 .
5. CONCLUSIONS This paper advances a robust method designed to watermark colour still image databases and extended towards colour video. Fig. 13: Stirmark attacked images.
The mark is embedded by means of a CDMA technique and spread over a sequence of images/frames, those making it possible for the trade-off between transparency and robustness to be met. Note that when designing this method we did not take into consideration any counter–attack, [25]. Moreover, we did not take advantage neither on error correcting codes, [26] nor on Wiener filtering. In fact, all these aspects are to improve the quality of our method. REFERENCES [1]. I. Cox, M. Miller, and J. Bloom, Digital Watermarking, Academic Press, 2002, ISBN 1-55860714-5. [2]. F. Petitcolas, R. Anderson, and M. Kuhn, “Information Hiding – A Survey”, in Proc. of the IEEE, Vol. 87 , No. 7, 1999, pp. 1062–1078. [3]. G. Langelaar, I. Setyawan, and R. Lagendijk, “Watermarking digital image and video data. A stateof-the-art overview” in the IEEE Signal Processing Magazine , Vol.17 No. 5, 2000, pp. 20-46. [4]. R. Wolfgang, and E. Delp, "Overview of Image Security Techniques with Applications in Multimedia Systems" in SPIE Vol. 3228, 1997, pp. 297-308. [5]. I. Cox, M. Miller, and J. Bloom, "Watermarking Applications and Their Properties", in Proc. of the International Conference on Information Technology: Coding and Computing - ITCC2000, 2000, pp. 6-10. [6]. D. Simitopoulos, et al, “Digital watermarking of MPEG-1 and MPEG-2 multiplexed streams for copyright protection” in Proc. of the Digital and Computational Video, 2001, pp.140 –147. [7]. F. Pérez-González, and J. Hernández, “A tutorial on digital watermarking” in Proc. of the 33rd IEEE Annual Carnahan Conference on Security Technology, Madrid, Spain, October 1999. [8]. P. Moulin, “The role of information theory in watermarking and its application to image watermarking” in Signal Processing, Vol. 81, No. 6, 2001, pp. 1121-1139. [9]. I. Cox, M. Miller, and A. McKellips, "Watermarking as Communications with Side Information" in Proc. of the IEEE, 87(7), 1999, pp. 1127-1141. [10]. Y. Steinberg, and N. Merhav, “Identification in the presence of side information with application to watermarking” in the IEEE Transactions on Information Theory, Vol. 47, No. 4, 2001, pp. 1410 –1422. [11]. F. Pérez-González, J.Hernández, and F. Balado, “Approaching the capacity limit in image watermarking: a perspective on coding techniques for
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